65ed4
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Prime factorization
5 × 13
Step size
36.9231¢
Octave
33\65ed4 (1218.46¢)
Twelfth
52\65ed4 (1920¢) (→4\5ed4)
Consistency limit
1
Distinct consistency limit
1
 |
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| ← 63ed4 | 65ed4 | 67ed4 → |
65 equal divisions of the 4th harmonic (abbreviated 65ed4) is a nonoctave tuning system that divides the interval of 4/1 into 65 equal parts of about 36.9 ¢ each. Each step represents a frequency ratio of 41/65, or the 65th root of 4.
Intervals
| Steps | Cents | Approximate Ratios |
|---|---|---|
| 0 | 0 | 1/1 |
| 1 | 36.923 | |
| 2 | 73.846 | 23/22 |
| 3 | 110.769 | 33/31 |
| 4 | 147.692 | |
| 5 | 184.615 | |
| 6 | 221.538 | 33/29 |
| 7 | 258.462 | |
| 8 | 295.385 | |
| 9 | 332.308 | 17/14, 23/19 |
| 10 | 369.231 | 21/17, 26/21 |
| 11 | 406.154 | 19/15 |
| 12 | 443.077 | 22/17 |
| 13 | 480 | 29/22 |
| 14 | 516.923 | 31/23 |
| 15 | 553.846 | |
| 16 | 590.769 | 31/22 |
| 17 | 627.692 | 33/23 |
| 18 | 664.615 | 22/15 |
| 19 | 701.538 | 3/2 |
| 20 | 738.462 | 23/15, 26/17 |
| 21 | 775.385 | |
| 22 | 812.308 | |
| 23 | 849.231 | 31/19 |
| 24 | 886.154 | |
| 25 | 923.077 | 29/17 |
| 26 | 960 | |
| 27 | 996.923 | |
| 28 | 1033.846 | |
| 29 | 1070.769 | 13/7 |
| 30 | 1107.692 | 19/10 |
| 31 | 1144.615 | 29/15, 33/17 |
| 32 | 1181.538 | |
| 33 | 1218.462 | |
| 34 | 1255.385 | 31/15 |
| 35 | 1292.308 | |
| 36 | 1329.231 | |
| 37 | 1366.154 | 11/5 |
| 38 | 1403.077 | 9/4 |
| 39 | 1440 | 23/10 |
| 40 | 1476.923 | |
| 41 | 1513.846 | |
| 42 | 1550.769 | |
| 43 | 1587.692 | |
| 44 | 1624.615 | |
| 45 | 1661.538 | |
| 46 | 1698.462 | |
| 47 | 1735.385 | |
| 48 | 1772.308 | |
| 49 | 1809.231 | |
| 50 | 1846.154 | 29/10 |
| 51 | 1883.077 | |
| 52 | 1920 | |
| 53 | 1956.923 | 31/10 |
| 54 | 1993.846 | |
| 55 | 2030.769 | |
| 56 | 2067.692 | 33/10 |
| 57 | 2104.615 | 27/8 |
| 58 | 2141.538 | |
| 59 | 2178.462 | |
| 60 | 2215.385 | |
| 61 | 2252.308 | |
| 62 | 2289.231 | |
| 63 | 2326.154 | |
| 64 | 2363.077 | |
| 65 | 2400 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +18.5 | +18.0 | +0.0 | -17.1 | -0.4 | -8.8 | +18.5 | -0.8 | +1.4 | -15.9 | +18.0 |
| Relative (%) | +50.0 | +48.9 | +0.0 | -46.3 | -1.1 | -23.9 | +50.0 | -2.3 | +3.7 | -43.2 | +48.9 | |
| Steps (reduced) |
33 (33) |
52 (52) |
65 (0) |
75 (10) |
84 (19) |
91 (26) |
98 (33) |
103 (38) |
108 (43) |
112 (47) |
117 (52) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -9.8 | +9.6 | +1.0 | +0.0 | +5.8 | +17.6 | -2.1 | -17.1 | +9.2 | +2.5 | -0.6 |
| Relative (%) | -26.4 | +26.1 | +2.6 | +0.0 | +15.7 | +47.7 | -5.8 | -46.3 | +25.0 | +6.8 | -1.6 | |
| Steps (reduced) |
120 (55) |
124 (59) |
127 (62) |
130 (0) |
133 (3) |
136 (6) |
138 (8) |
140 (10) |
143 (13) |
145 (15) |
147 (17) | |